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Cryptanalysis of a digital signature scheme of W. He.

Wong, Chun Kuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 43-45). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Origin of The First Digital Signature Scheme --- p.2 / Chapter 1.2 --- On the security of digital signature schemes --- p.3 / Chapter 1.3 --- Organization of the Thesis --- p.4 / Chapter 2 --- Mathematical Background --- p.6 / Chapter 2.1 --- Divisibility --- p.6 / Chapter 2.2 --- Prime --- p.7 / Chapter 2.3 --- Modular arithmetic --- p.7 / Chapter 2.4 --- Congruence --- p.7 / Chapter 2.5 --- Greatest Common Divisor --- p.7 / Chapter 2.6 --- Integers modulo n --- p.8 / Chapter 2.7 --- Inverse --- p.8 / Chapter 2.8 --- Division in Zn --- p.8 / Chapter 2.9 --- Order of element --- p.8 / Chapter 2.10 --- Euclidean Algorithm --- p.9 / Chapter 2.11 --- Extended Euclidean Algorithm --- p.9 / Chapter 2.12 --- Chinese Remainder Theorem --- p.10 / Chapter 2.13 --- Relatively Prime --- p.10 / Chapter 2.14 --- Euler Totient Function --- p.10 / Chapter 2.15 --- Fermat's Little Theorem --- p.11 / Chapter 2.16 --- Euler's Theorem --- p.11 / Chapter 2.17 --- Square root --- p.12 / Chapter 2.18 --- Quadratic residue --- p.12 / Chapter 2.19 --- Legendre Symbol --- p.13 / Chapter 2.20 --- Jacobi Symbol --- p.14 / Chapter 2.21 --- Blum Integer --- p.15 / Chapter 2.22 --- The Factoring Problem --- p.16 / Chapter 2.23 --- The Discrete Logarithm Problem --- p.17 / Chapter 2.24 --- One-way Hash Function --- p.17 / Chapter 3 --- Survey of digital signature schemes --- p.19 / Chapter 3.1 --- The RSA signature scheme --- p.19 / Chapter 3.1.1 --- Key generation in the RSA signature scheme --- p.20 / Chapter 3.1.2 --- Signature generation in the RSA signature scheme --- p.20 / Chapter 3.1.3 --- Signature verification in the RSA signature scheme --- p.20 / Chapter 3.1.4 --- On the security of the RSA signature scheme --- p.21 / Chapter 3.2 --- The ElGamal signature scheme --- p.22 / Chapter 3.2.1 --- Key generation in the ElGamal signature scheme --- p.23 / Chapter 3.2.2 --- Signature generation in the ElGamal signature scheme --- p.23 / Chapter 3.2.3 --- Signature verification in the ElGamal signature scheme --- p.23 / Chapter 3.2.4 --- On the security of the ElGamal signature scheme --- p.24 / Chapter 3.3 --- The Schnorr signature scheme --- p.26 / Chapter 3.3.1 --- Key generation in the Schnorr signature scheme --- p.26 / Chapter 3.3.2 --- Signature generation in the Schnorr signature scheme --- p.26 / Chapter 3.3.3 --- Signature verification in the Schnorr signature scheme --- p.27 / Chapter 3.3.4 --- Discussion --- p.27 / Chapter 3.4 --- Digital signature schemes based on both the factoring and discrete logarithm problems --- p.27 / Chapter 3.4.1 --- The Brickell-McCurley signature scheme --- p.28 / Chapter 3.4.2 --- The Okamoto signature scheme --- p.29 / Chapter 3.4.3 --- The Harn signature scheme --- p.30 / Chapter 3.4.4 --- The Shao signature scheme --- p.30 / Chapter 3.4.5 --- The W. He signature scheme --- p.31 / Chapter 4 --- Cryptanalysis of the digital signature scheme of W. He --- p.32 / Chapter 4.1 --- The Digital Signature Scheme of W. He --- p.33 / Chapter 4.1.1 --- System setup in the W. He Digital Signature Scheme --- p.33 / Chapter 4.1.2 --- Key generation in the W. He Digital Signature Scheme --- p.34 / Chapter 4.1.3 --- Signature generation in the W. He Digital Signature Scheme --- p.34 / Chapter 4.1.4 --- Signature verification in the W. He Digital Signature Scheme --- p.34 / Chapter 4.2 --- Cryptanalysis of the digital signature scheme of W. He --- p.35 / Chapter 4.2.1 --- Theorems on the security of the digital signature scheme of W. He --- p.35 / Chapter 4.2.2 --- Signature Forgery in the digital signature scheme of W. He --- p.37 / Chapter 4.2.3 --- Remedy --- p.40 / Chapter 5 --- Conclusions --- p.41 / Bibliography --- p.43

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323962
Date January 2002
ContributorsWong, Chun Kuen., Chinese University of Hong Kong Graduate School. Division of Information Engineering.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, bibliography
Formatprint, ix, 45 leaves ; 30 cm.
RightsUse of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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